You don't have to be Indiana Jones to have fun with archaeology. Marcus Brody had fun too. Arranging the Inca artifacts in an order of chronologies so they paired nicely with the Maya and Greek.
Museum sees you as a Marcus, responsible for sending Indy out to collect items from around the world and then hand them to you, so you can place them in a Museum that you are responsible for.
Yes, you don't actually own the Museum, your working for your patron, who donates a lot of money. So therefore, they want the displays to be centered around their loves of history. That doesn't mean that you can't put whatever you want or sometime, whatever you can get your hands on. But it does help if you can please them too.
Paying to get these precious items into glass cabinets is an expensive affair. You will have to place another magnificent item or items into a storage to be able to place the object you want on display. No historical object is lost as you can dig them out of storage later, as can the other players. They may have eyes on that "Arc of the Covenant." Or you could sacrifice some of your hard earned prestige to help with the cost.
Here are some of the 180 objects that can be found.